Thanks for these perfectly consistent replies - I didn't understand the purpose of m = sum(w * f/sum(w)) and saw it merely as a weighted average of the fitted values.
My ultimate concern is how to compute an appropriate weighted TSS (or equivalently, MSS) for PRESS-R^2 = 1 - PRESS/TSS = 1 - PRESS/ (MSS + PRESS). Do you think it then makes sense to substitute the vector of leave-one-out fitted values for f here? m <- sum(w * f/sum(w)) mss <- sum(w * (f - m)^2) Murray ________________________________________ From: peter dalgaard <[email protected]> Sent: Friday, 8 April 2016 11:28 p.m. To: Duncan Murdoch Cc: Murray Efford; [email protected] Subject: Re: [R] R.squared in summary.lm with weights On 08 Apr 2016, at 12:57 , Duncan Murdoch <[email protected]> wrote: > On 07/04/2016 5:21 PM, Murray Efford wrote: >> Following some old advice on this list, I have been reading the code for >> summary.lm to understand the computation of R-squared from a weighted >> regression. Usually weights in lm are applied to squared residuals, but I >> see that the weighted mean of the observations is calculated as if the >> weights are on the original scale: >> >> [...] >> f <- z$fitted.values >> w <- z$weights >> [...] >> m <- sum(w * f/sum(w)) >> [mss <-] sum(w * (f - m)^2) >> [...] >> >> This seems inconsistent to me. What am I missing? > > I think you are expecting consistency where there needn't be any. Why do you > see an inconsistency here? Those are different calculations. You get > expressions like these if you assume observations have variance sigma^2/w, > and you're trying to estimate sigma^2. > It's also perfectly consistent that m is the minimizer of mss: d/dm sum(w*(f-m)^2) = -2 sum(w*(f-m)) = 0 => m = sum(w*f) / sum(w) However, beware the distiction between inverse variance weights, replication weights, and sampling weights. > Duncan Murdoch > > ______________________________________________ > [email protected] mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: [email protected] Priv: [email protected] ______________________________________________ [email protected] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
